A164298 - OEIS

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A164298

a(n) = ((1+4*sqrt(2))*(2+sqrt(2))^n + (1-4*sqrt(2))*(2-sqrt(2))^n)/2.

1, 10, 38, 132, 452, 1544, 5272, 18000, 61456, 209824, 716384, 2445888, 8350784, 28511360, 97343872, 332352768, 1134723328, 3874187776, 13227304448, 45160842240, 154188760064, 526433355776, 1797355902976, 6136556900352 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`Binomial transform of A048696. Second binomial transform of A164587. Inverse binomial transform of A164299.`
	LINKS	`Table of n, a(n) for n=0..23.`
	FORMULA	`a(n) = 4a(n-1)-2a(n-2) for n > 1; a(0)=1, a(1)=10.` `G.f.: (1+6x)/(1-4x+2*x^2).`
	PROG	`(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+4r)(2+r)^n+(1-4r)(2-r)^n)/2: n in [0..27] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus, Aug 17 2009]`
	CROSSREFS	`Cf. A048696, A164587, A164299.` `Sequence in context: A136840 A027982 A064603 * A050479 A220206 A218081` `Adjacent sequences: A164295 A164296 A164297 * A164299 A164300 A164301`
	KEYWORD	`nonn`
	AUTHOR	`Al Hakanson (hawkuu(AT)gmail.com), Aug 12 2009`
	EXTENSIONS	`Edited and extended beyond a(5) by Klaus Brockhaus, Aug 17 2009`
	STATUS	`approved`

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Last modified May 20 01:43 EDT 2013. Contains 225445 sequences.